Mapping starspots and magnetic fields on cool stars

Andrew Collier Cameron,Ron Hilditch, Moira Jardine and John Barnes, Tim Lister, Sandra Jeffers

Recent highlights:

The cool stars group at St Andrews uses indirect imaging methods, including Doppler tomography, Zeeman-Doppler imaging, eclipse mapping and prominence tomography to make maps of cool starspots and other magnetic structures on and above the surfaces of rapidly rotating stars. With Jean-Francois Donati (Toulouse) and Meir Semel (Meudon) we have established a world-leading long-term programme of Zeeman-Doppler imaging at the Anglo-Australian Telescope. This enables us to map changes in magnetic-field patterns on stellar surfaces from year to year. This programme also produced the first detailed measurements of surface differential rotation on stars other than the Sun, by enabling us to use starspots as tracers of large-scale fluid shear. We find that even in stars rotating 50 times faster than the Sun, the differential rotation rate is similar. We are using these powerful new observations to extend what we know about physics of similar structures on the Sun (spots, prominences, etc) to the much more densely-packed magnetic structures we see on other, more active stars. We now suspect that 40% or more of some starsí surfaces are covered in dark magnetic spots, and we are developing sensitive new eclipse-mapping methods to determine the packing fraction and size distribution of these structures.

How Doppler imaging works:

The term ``Doppler imaging'' was coined by Vogt & Penrod (1983), who demonstrated that travelling starspot bumps were observable in the line profiles of HR 1099, and that an image of the stellar surface could be derived from them. A photospheric absorption line in which rotation is the dominant broadening mechanism displays time-variable irregularities if the visible surface of the star is mottled by dark spots. The effect of a cool, dark region on a rotationally-broadened line profile is illustrated in Fig. 1.

Cartoon of starspot bump formation

Fig. 1: The ``missing'' light of the spot consists of a continuum contribution that spans the line profile, plus a narrow line contribution that is Doppler shifted by an amount that depends on the projected distance of the spot from the stellar rotation axis. Removing this light causes an overall depression of the continuum, but less light is removed at the Doppler shift of the spot relative to the centre of the line. The observable signature of a dark spot on the stellar surface is therefore a bright bump in every photospheric absorption line in the star's spectrum.
 As the star rotates, the spots are carried across the stellar disc, causing the bumps to change their Doppler shifts in accordance with their projected distances from the star's rotation axis. Spots near the equator remain visible for half the stellar rotation cycle, tracing out a sinusoidal velocity variation with an amplitude equal to the stellar equatorial rotation velocity, Vsini. Spots at progressively higher latitudes follow progressively lower-amplitude sinusoids. The fraction of the rotation cycle for which a spot remains visible depends on its latitude and the inclination of the stellar rotation axis to the line of sight. The times at which spot signatures cross the centre of the line profile thus reveal their longitudes, while the amplitudes of their sinusoids (or equivalently, their radial accelerations at line centre) tell us their latitudes.

For a fuller account of the technical details and recent results, the following resources are available:

Zeeman-Doppler imaging

This is a variant on the Doppler imaging technique. It uses circular and linear polarization information to measure the small shifts in wavelength and profile shape that arise in the presence of a magnetic field. Both the strength of the field and its orientation relative to the line of sight can be determined. As in conventional Doppler imaging, the rotation of the star is used to resolve different magnetic regions on the stellar surface. Jean-Francois Donati has an excellent web page describing this technique.

Eclipse mapping of starspots on magnetically active binaries

Many magnetically active stars are found in close binary systems, where one or both stars have been spun up by tidal interaction to an abnormally high rotation rate. If the system orbits nearly edge-on, eclipses will occur as one star passes in front of the other. Starspots on the eclipsed hemisphere of either star will distort the eclipse profile, giving it a jagged or "stepped" appearance from which the locations and sizes of the spots can be inferred. This technique works both for dark spots and for hotspots where an accretion stream originating in a semi-detached binary component impacts the inner face of its companion.


Tomographic eclipse map of starspots on the solar-type primary star of the short-period binary system XY Ursae Majoris.

Stellar prominences as tracers of coronal structure

Until about a decade ago, the substructures seen in the Balmer-line profiles of active stars were generally regarded as too complex for quantitative study. Since then, however, detector technology has improved to the point where we can monitor the evolution of these structures with temporal sampling rates high enough to allow us to see coherent patterns in the data.

Although some of the patterns that have emerged from such studies are consistent with stochastic flare activity, a large part of the complex substructure seen in the Balmer lines appears to be caused by mass motions of clumps of Balmer emitting and absorbing material. As these clumps are embedded in the much hotter ambient medium of the stellar corona, they are usually dubbed ``prominences" by analogy to solar prominences.

Some of the mass motions seen in association with stellar flares are transient, and appear to resemble the prominence eruptions seen on the Sun in connection with coronal mass ejections and two-ribbon flares. Others appear to be more akin to solar quiescent prominences, persisting over several stellar rotations in more or less the same location. In these cases, the change in rotational Doppler shift with viewing angle can be used to extract information about the physical locations of the emitting or absorbing structures.

Observational examples of prominence-like activity are found in both single and binary stars. The St Andrews group's efforts in this area concern the spatial relationships between prominences and underlying features on the stellar surface. We are finding them to be powerful probes of the fine spatial structure of stellar coronal magnetic fields, in a way that cannot be achieved with X-ray studies.